






"""simple docstring"""
def 							snake_case (  A__      ,A__		):
			if a < 0 or b < 0:
						raise ValueError("the value of both inputs must be positive"		)

			UpperCAmelCase_	:					str     	=   str(bin(A__		)		)[2:]  # remove the leading "0b"
			UpperCAmelCase_	:					Optional[int]     	=   str(bin(A__		)		)[2:]  # remove the leading "0b"

			UpperCAmelCase_	:					str     	=   max(len(A__		)      ,len(A__		)		)

			return "0b" + "".join(
			    str(int(char_a == "1" and char_b == "1"		)		)
			    for char_a, char_b in zip(a_binary.zfill(A__		)      ,b_binary.zfill(A__		)		)		)


if __name__ == "__main__":
			import doctest

			doctest.testmod()











"""simple docstring"""
def 							A						(				__snake_case: int = 1_0_0_0_0_0_0  )    ->		int:

       """simple docstring"""





       __magic_name__      				=    limit + 1
       __magic_name__      				=    [0] * limit
       for first_term in range(1 ,     __snake_case  ):
              for n in range(__snake_case ,     __snake_case ,     __snake_case  ):
                     __magic_name__      				=    first_term + n / first_term
                     if common_difference % 4:  # d must be divisble by 4
                            continue
                     else:
                            common_difference /= 4
                            if (
                                first_term > common_difference
                                and first_term < 4 * common_difference
                            ):  # since x,y,z are positive integers
                                   frequency[n] += 1  # so z>0 and a>d ,also 4d<a

       __magic_name__      				=    sum(1 for x in frequency[1:limit] if x == 1_0  )

       return count


if __name__ == "__main__":
 print(f"""{solution() = }""")